Tangle replacements and knot Floer homology torsions

We show that the torsion order of a knot in the corresponding knot Floer homology group gives a lower bound for the minimum number such that an oriented ‐tangle replacement unknots . This generalizes earlier results by Alishahi and the author and by Juhász, Miller and Zemke, that is a lower bound for both the unknotting number and for , where is the bridge index of .